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</p><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="38" class="slide " data-line="38" data-h="1" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>大纲</h5></div></div>
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</p><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="46" class="slide " data-line="46" data-h="1" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>背景</h5></div></div>
<br>
<p>维纳 《控制论》：</p>
<br>
<blockquote>
<p>第一次工业革命：用某种机器来减轻甚至代替<span class="blue">体力</span>劳动</p>
</blockquote>
<blockquote>
<p>上世纪中叶：用某种新型机器来减轻甚至代替某些<span class="blue">脑力</span>劳动</p>
</blockquote>
<br>
<p>关键：让机器具有人类的智能</p>
<br>
<p>问题：什么是智能？</p>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="70" class="slide " data-line="70" data-h="1" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>起源</h5></div></div>
<p>《Computing Machinery and Intelligence》</p>
<div class="width62 left0 right0 top2 bottom2">
<p>图灵在他 1950 年的这篇论文中提出了<span class="blue">图灵测试</span>：一个人在不接触对方的情况下，通过一种特殊的方式，和对方进行一系列的问答，如果在相当长时间内，他无法根据这些问题判断对方是人还是计算机，那么就可以认为这个计算机是智能的</p>
</div>
<p>要想通过图灵测试，机器得具备多种能力</p>
<ul>
<li>学习：机器学习</li>
<li>感知：计算机视觉，语音识别</li>
<li>认知：自然语言处理，知识表示</li>
</ul>
<img src="../common/img/turing.jpg" title="图灵" style="margin-right:4rem;margin-left:auto;margin-top:-28rem;width:30%">
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="92" class="slide " data-line="92" data-h="1" data-v="3">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>元年</h5></div></div>
<p>达特茅斯会议</p>
<ul>
<li>时间：1956 年</li>
<li>地点：达特茅斯学院</li>
<li>人物：香农、麦卡锡、明斯基、西蒙、纽厄尔等十人</li>
<li>事件：讨论用机器模拟人的智能</li>
</ul>
<br>
<div class="multi_column top_2">
    <img src="../common/img/birth-school.jpg" title="达特茅斯学院" width="425px" height="277px" style="margin-left:3rem">
    <img src="../common/img/birth-people.jpg" title="2006年会议50周年时还健在的5位参会者" width="425px" height="277px" style="margin-right:3rem;margin-left:auto">
</div>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="112" class="slide " data-line="112" data-h="1" data-v="4">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>发展</h5></div></div>
<div class="mermaid">gantt
todayMarker off
dateFormat YYYY
axisFormat %Y
title 人工智能的三次浪潮

section 史前文明

推理期: done, 1950, 1965
1950 图灵测试: 1950, milestone
1956 达特茅斯会议: 1956, milestone

知识期: done, 1969, 1987
1969 知识系统兴起: 1969, milestone
1980 专家系统兴起: 1980, milestone

学习期: active, 1985, 2021
1995 统计学习兴起: 1995, milestone
2012 深度学习兴起: 2012, milestone
</div><p>秽土转生</p>
<ul>
<li>推理：反绎学习，图神经网络</li>
<li>知识：知识图谱，图神经网络</li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="125" class="slide " data-line="125" data-h="2" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>推理期</h5></div></div>
<p>机器擅长固定套路的计算 vs. 人类擅长妙手偶得的推理</p>
<div class="bottom4"></div>
<p>符号主义：<span class="blue">智能 = 逻辑推理</span></p>
<div class="bottom4"></div>
<p>西蒙和纽厄尔设计了<span class="blue">逻辑理论家</span>程序</p>
<ul>
<li>1952 年，逻辑理论家证明了 《数学原理》 中的 38 条定理</li>
<li>1963 年，证明了全部 52 条定理，其中定理 2.85 的证明比原书作者更巧妙</li>
<li>西蒙和纽厄尔获得了 1975 年的图灵奖</li>
</ul>
<div class="bottom4"></div>
<p>衰退：</p>
<ul>
<li>并非所有定理都可以方便地符号化，也并非所有问题都可以转换成推理问题</li>
<li>十万步内无法证明<span class="blue">两个连续函数之和还是连续函数</span></li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="152" class="slide " data-line="152" data-h="2" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>符号主义</h5></div></div>
<p>根据以下事实判别谁说了实话</p>
<ul>
<li><span class="mathjax-exps">$A$</span>：<span class="mathjax-exps">$B$</span>和<span class="mathjax-exps">$C$</span>都是说谎者</li>
<li><span class="mathjax-exps">$B$</span>：<span class="mathjax-exps">$A$</span>和<span class="mathjax-exps">$C$</span>都是说谎者</li>
<li><span class="mathjax-exps">$C$</span>：<span class="mathjax-exps">$A$</span>和<span class="mathjax-exps">$B$</span>中至少有一个说谎者</li>
</ul>
<div class="threelines row7-border-top-solid column1-border-right-solid">
<table>
<thead>
<tr>
<th style="text-align:center">公式</th>
<th style="text-align:center"><span class="mathjax-exps">$p \rightarrow q$</span></th>
<th style="text-align:center"><span class="mathjax-exps">$\Longleftrightarrow$</span></th>
<th style="text-align:center"><span class="mathjax-exps">$\neg p \vee q$</span></th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><strong>条件</strong></td>
<td style="text-align:center"><span class="mathjax-exps">$A \rightarrow \neg B \wedge \neg C$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$\Longleftrightarrow$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$1.~\neg A \vee \neg B, \quad 2.~\neg A \vee \neg C$</span></td>
</tr>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center"><span class="mathjax-exps">$\neg A \rightarrow B \vee C$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$\Longleftrightarrow$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$3.~A \vee B \vee C$</span></td>
</tr>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center"><span class="mathjax-exps">$B \rightarrow \neg A \wedge \neg C$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$\Longleftrightarrow$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$4.~\neg B \vee \neg C$</span></td>
</tr>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center"><span class="mathjax-exps">$\neg B \rightarrow A \vee C$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$\Longleftrightarrow$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$3.~A \vee B \vee C$</span></td>
</tr>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center"><span class="mathjax-exps">$C \rightarrow \neg A \vee \neg B$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$\Longleftrightarrow$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$5.~\neg A \vee \neg B \vee \neg C$</span></td>
</tr>
<tr>
<td style="text-align:center"></td>
<td style="text-align:center"><span class="mathjax-exps">$\neg C \rightarrow A \wedge B$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$\Longleftrightarrow$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$6.~A \vee C, \quad 7.~B \vee C$</span></td>
</tr>
<tr>
<td style="text-align:center"><strong>归结</strong></td>
<td style="text-align:center"><span class="mathjax-exps">$1 + 7 \rightarrow 8.~\neg A \vee C$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$\Longleftrightarrow$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$C$</span>说了实话</td>
</tr>
</tbody>
</table>
</div>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="178" class="slide " data-line="178" data-h="2" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>知识期</h5></div></div>
<p>教训：光有逻辑推理远远不够，机器得拥有知识</p>
<div class="bottom4"></div>
<p>信仰：知识就是力量，<span class="blue">智能 = 知识 + 逻辑推理</span></p>
<div class="bottom4"></div>
<p>专家系统 = 知识库 + 推理机</p>
<ul>
<li>在特定领域内具有专家水平解决问题能力的程序系统</li>
<li>第一个成功的专家系统 DENDRAL 于 1968 年问世</li>
<li>知识工程之父费根鲍姆获得了 1994 年的图灵奖</li>
</ul>
<div class="bottom4"></div>
<p>衰退：</p>
<ul>
<li>人工构建知识库成本太高</li>
<li>很多知识获取困难，甚至无法被清晰地表示出来</li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="205" class="slide " data-line="205" data-h="2" data-v="3">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>动物识别专家系统</h5></div></div>
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</p><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="213" class="slide " data-line="213" data-h="3" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>学习期</h5></div></div>
<p>基本想法：让<span class="blue">机器</span>从数据中自动<span class="blue">学习</span>得到某种知识 (规律)</p>
<p>基本流程：</p>
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<p>原始数据：图片、视频、文本、语音、……</p>
<p>特征工程：</p>
<ul>
<li>提取：选取对目标任务有用的潜在特征，如对西瓜提取色泽、根蒂、敲声等</li>
<li>处理：无序的离散类别特征 → 数值特征，特征缺失处理，特征标准化</li>
<li>变换：对特征进行挑选或映射得到对目标任务更有效的特征</li>
</ul>
<p>模型学习：机器学习最核心的部分，学习一个特征到类别标记的映射</p>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="237" class="slide " data-line="237" data-h="3" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征提取 以文本为例</h5></div></div>
<p><span class="blue">词袋模型</span> (bag-of-words)：文本是单词的集合，单词间独立、无序</p>
<p>所有文本全部<span class="mathjax-exps">$d$</span>个不同的单词构成词典，每个文本提取<span class="mathjax-exps">$d$</span>个特征</p>
<p>若词典第<span class="mathjax-exps">$i$</span>个词在当前文本中出现过，则其第<span class="mathjax-exps">$i$</span>个特征为<span class="mathjax-exps">$1$</span>，否则为<span class="mathjax-exps">$0$</span></p>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>feature_extraction<span class="token punctuation">.</span>text <span class="token keyword">import</span> CountVectorizer
<span class="token keyword">import</span> pandas <span class="token keyword">as</span> pd

document1 <span class="token operator">=</span> <span class="token string">"I have a pen, I have an apple, apple pen."</span>
document2 <span class="token operator">=</span> <span class="token string">"I have a pen, I have pineapple, pineapple pen."</span>
cv <span class="token operator">=</span> CountVectorizer<span class="token punctuation">(</span>lowercase<span class="token operator">=</span><span class="token boolean">False</span><span class="token punctuation">,</span> token_pattern<span class="token operator">=</span><span class="token string">'\w+'</span><span class="token punctuation">,</span> binary<span class="token operator">=</span><span class="token boolean">True</span><span class="token punctuation">)</span>
model <span class="token operator">=</span> cv<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span><span class="token punctuation">[</span>document1<span class="token punctuation">,</span> document2<span class="token punctuation">]</span><span class="token punctuation">)</span>
pd<span class="token punctuation">.</span>DataFrame<span class="token punctuation">(</span>model<span class="token punctuation">.</span>toarray<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span> columns<span class="token operator">=</span>cv<span class="token punctuation">.</span>get_feature_names_out<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="threelines column1-border-right-solid column1-bold head-highlight-1 tr-hover top-4">
<table>
<thead>
<tr>
<th style="text-align:center">词典</th>
<th style="text-align:center">I</th>
<th style="text-align:center">a</th>
<th style="text-align:center">an</th>
<th style="text-align:center">apple</th>
<th style="text-align:center">have</th>
<th style="text-align:center">pen</th>
<th style="text-align:center">pineapple</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">文本 1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">0</td>
</tr>
<tr>
<td style="text-align:center">文本 2</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">0</td>
<td style="text-align:center">0</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
</tr>
</tbody>
</table>
</div>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="269" class="slide " data-line="269" data-h="3" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征提取 以文本为例</h5></div></div>
<p><span class="blue">词袋模型</span> (bag-of-words)：文本是单词的集合，单词间独立、无序</p>
<p>所有文本全部<span class="mathjax-exps">$d$</span>个不同的单词构成词典，每个文本提取<span class="mathjax-exps">$d$</span>个特征</p>
<p>若词典第<span class="mathjax-exps">$i$</span>个词在当前文本中出现了<span class="mathjax-exps">$k$</span>次，则其第<span class="mathjax-exps">$i$</span>个特征为<span class="mathjax-exps">$k$</span></p>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>feature_extraction<span class="token punctuation">.</span>text <span class="token keyword">import</span> CountVectorizer
<span class="token keyword">import</span> pandas <span class="token keyword">as</span> pd

document1 <span class="token operator">=</span> <span class="token string">"I have a pen, I have an apple, apple pen."</span>
document2 <span class="token operator">=</span> <span class="token string">"I have a pen, I have pineapple, pineapple pen."</span>
cv <span class="token operator">=</span> CountVectorizer<span class="token punctuation">(</span>lowercase<span class="token operator">=</span><span class="token boolean">False</span><span class="token punctuation">,</span> token_pattern<span class="token operator">=</span><span class="token string">'\w+'</span><span class="token punctuation">)</span>
model <span class="token operator">=</span> cv<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span><span class="token punctuation">[</span>document1<span class="token punctuation">,</span> document2<span class="token punctuation">]</span><span class="token punctuation">)</span>
pd<span class="token punctuation">.</span>DataFrame<span class="token punctuation">(</span>model<span class="token punctuation">.</span>toarray<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span> columns<span class="token operator">=</span>cv<span class="token punctuation">.</span>get_feature_names_out<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="threelines column1-border-right-solid column1-bold head-highlight-1 tr-hover top-4">
<table>
<thead>
<tr>
<th style="text-align:center">词典</th>
<th style="text-align:center">I</th>
<th style="text-align:center">a</th>
<th style="text-align:center">an</th>
<th style="text-align:center">apple</th>
<th style="text-align:center">have</th>
<th style="text-align:center">pen</th>
<th style="text-align:center">pineapple</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">文本 1</td>
<td style="text-align:center">2</td>
<td style="text-align:center">1</td>
<td style="text-align:center">1</td>
<td style="text-align:center">2</td>
<td style="text-align:center">2</td>
<td style="text-align:center">2</td>
<td style="text-align:center">0</td>
</tr>
<tr>
<td style="text-align:center">文本 2</td>
<td style="text-align:center">2</td>
<td style="text-align:center">1</td>
<td style="text-align:center">0</td>
<td style="text-align:center">0</td>
<td style="text-align:center">2</td>
<td style="text-align:center">2</td>
<td style="text-align:center">2</td>
</tr>
</tbody>
</table>
</div>
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</section><section vertical="true" data-notes="" lineno="301" class="slide " data-line="301" data-h="3" data-v="3">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征提取 以文本为例</h5></div></div>
<p><span class="blue">词袋模型</span> (bag-of-words)：文本是单词的集合，单词间独立、无序</p>
<p>所有文本全部<span class="mathjax-exps">$d$</span>个不同的单词构成词典，每个文本提取<span class="mathjax-exps">$d$</span>个特征</p>
<p><span class="blue">词频 - 逆文本频率</span>特征：对当前文本重要的单词必然</p>
<ul>
<li>在当前文本中出现的频率高，即词频 (term frequency, tf) 高</li>
<li>在其他文本中出现的频率低，即逆文本频率 (inverse document frequency, idf) 高</li>
</ul>
<p>tf = 单词在当前文本中出现的次数 / 当前文本的总词数</p>
<p>idf = ln ((全部文本数 + C) / (包含该词的总文本数 + C)) + 1</p>
<ul>
<li>C = 0，若词典包含从未在任何文本中出现的词，会有分母为零的问题</li>
<li>C = 1，sklearn 中默认采用的平滑版本，相当于额外有一个包含所有词的文本</li>
</ul>
<p>tf - idf 特征 = normalize (tf × idf)，即将 tf 和 idf 相乘后再标准化</p>
<ul>
<li><span class="mathjax-exps">$\ell_1$</span>标准化，tf × idf / sum (tf × idf)，即线性变换成概率分布</li>
<li><span class="mathjax-exps">$\ell_2$</span>标准化，tf × idf / sqrt(sum ([tf × idf]^2))，即线性变换成模为 1 的向量</li>
</ul>
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</section><section vertical="true" data-notes="" lineno="328" class="slide " data-line="328" data-h="3" data-v="4">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征提取 以文本为例</h5></div></div>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>feature_extraction<span class="token punctuation">.</span>text <span class="token keyword">import</span> TfidfVectorizer
<span class="token keyword">import</span> pandas <span class="token keyword">as</span> pd

document1 <span class="token operator">=</span> <span class="token string">"I have a pen, I have an apple, apple pen."</span>
document2 <span class="token operator">=</span> <span class="token string">"I have a pen, I have pineapple, pineapple pen."</span>
tv <span class="token operator">=</span> TfidfVectorizer<span class="token punctuation">(</span>lowercase<span class="token operator">=</span><span class="token boolean">False</span><span class="token punctuation">,</span> token_pattern<span class="token operator">=</span><span class="token string">'\w+'</span><span class="token punctuation">,</span>
                     norm<span class="token operator">=</span><span class="token string">'l1'</span><span class="token punctuation">,</span> smooth_idf<span class="token operator">=</span><span class="token boolean">False</span><span class="token punctuation">)</span> <span class="token comment"># l1归一化 idf不平滑</span>
model <span class="token operator">=</span> tv<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span><span class="token punctuation">[</span>document1<span class="token punctuation">,</span> document2<span class="token punctuation">]</span><span class="token punctuation">)</span>
pd<span class="token punctuation">.</span>DataFrame<span class="token punctuation">(</span>model<span class="token punctuation">.</span>toarray<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span> columns<span class="token operator">=</span>cv<span class="token punctuation">.</span>get_feature_names_out<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="threelines row3-border-top-dashed row3-border-bottom-dashed column1-border1-right-dashed-head row1-column1-border1-right-dashed row3-column1-border1-right-dashed row4-column1-border1-right-dashed head-highlight-1 tr-hover top-4">
<table>
<thead>
<tr>
<th style="text-align:center">词典</th>
<th style="text-align:center">I</th>
<th style="text-align:center">a</th>
<th style="text-align:center">an</th>
<th style="text-align:center">apple</th>
<th style="text-align:center">have</th>
<th style="text-align:center">pen</th>
<th style="text-align:center">pineapple</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center" rowspan="2">tf</td>
<td style="text-align:center">2 / 10</td>
<td style="text-align:center">1 / 10</td>
<td style="text-align:center">1 / 10</td>
<td style="text-align:center">2 / 10</td>
<td style="text-align:center">2 / 10</td>
<td style="text-align:center">2 / 10</td>
<td style="text-align:center">0</td>
</tr>
<tr>

<td style="text-align:center">2 / 9</td>
<td style="text-align:center">1 / 9</td>
<td style="text-align:center">0</td>
<td style="text-align:center">0</td>
<td style="text-align:center">2 / 9</td>
<td style="text-align:center">2 / 9</td>
<td style="text-align:center">2 / 9</td>
</tr>
<tr>
<td style="text-align:center">idf</td>
<td style="text-align:center">ln (1) + 1</td>
<td style="text-align:center">ln (1) + 1</td>
<td style="text-align:center">ln (2) + 1</td>
<td style="text-align:center">ln (2) + 1</td>
<td style="text-align:center">ln (1) + 1</td>
<td style="text-align:center">ln (1) + 1</td>
<td style="text-align:center">ln (2) + 1</td>
</tr>
<tr>
<td style="text-align:center" rowspan="2">tf - idf</td>
<td style="text-align:center">0.165571</td>
<td style="text-align:center">0.082785</td>
<td style="text-align:center">0.140168</td>
<td style="text-align:center">0.280335</td>
<td style="text-align:center">0.165571</td>
<td style="text-align:center">0.165571</td>
<td style="text-align:center">0.000000</td>
</tr>
<tr>

<td style="text-align:center">0.192561</td>
<td style="text-align:center">0.096281</td>
<td style="text-align:center">0.000000</td>
<td style="text-align:center">0.000000</td>
<td style="text-align:center">0.192561</td>
<td style="text-align:center">0.192561</td>
<td style="text-align:center">0.326035</td>
</tr>
</tbody>
</table>
</div>
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</section></section><section><section data-notes="" lineno="358" class="slide " data-line="358" data-h="4" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征 离散类别 → 数值</h5></div></div>
<div class="threelines column9-border-right-solid head-highlight-1 tr-hover">
<table>
<thead>
<tr>
<th style="text-align:center">编号</th>
<th style="text-align:center">色泽</th>
<th style="text-align:center">根蒂</th>
<th style="text-align:center">敲声</th>
<th style="text-align:center">纹理</th>
<th style="text-align:center">脐部</th>
<th style="text-align:center">触感</th>
<th style="text-align:center">密度</th>
<th style="text-align:center">含糖率</th>
<th style="text-align:center">好瓜</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">1</td>
<td style="text-align:center">青绿</td>
<td style="text-align:center">蜷缩</td>
<td style="text-align:center">浊响</td>
<td style="text-align:center">清晰</td>
<td style="text-align:center">凹陷</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.697</td>
<td style="text-align:center">0.460</td>
<td style="text-align:center">是</td>
</tr>
<tr>
<td style="text-align:center">2</td>
<td style="text-align:center">乌黑</td>
<td style="text-align:center">蜷缩</td>
<td style="text-align:center">沉闷</td>
<td style="text-align:center">清晰</td>
<td style="text-align:center">凹陷</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.774</td>
<td style="text-align:center">0.376</td>
<td style="text-align:center">是</td>
</tr>
<tr>
<td style="text-align:center">3</td>
<td style="text-align:center">乌黑</td>
<td style="text-align:center">稍蜷</td>
<td style="text-align:center">沉闷</td>
<td style="text-align:center">稍糊</td>
<td style="text-align:center">稍凹</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.666</td>
<td style="text-align:center">0.091</td>
<td style="text-align:center">否</td>
</tr>
<tr>
<td style="text-align:center">4</td>
<td style="text-align:center">浅白</td>
<td style="text-align:center">硬挺</td>
<td style="text-align:center">清脆</td>
<td style="text-align:center">模糊</td>
<td style="text-align:center">平坦</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.245</td>
<td style="text-align:center">0.057</td>
<td style="text-align:center">否</td>
</tr>
</tbody>
</table>
</div>
<p>三种重编码方式：</p>
<ul>
<li>序数编码 (ordinal encoding)：清晰 - 0、稍糊 - 1、模糊 - 2，<span class="blue">需类别特征本身有序</span>，否则若青绿 - 0、乌黑 - 1、浅白 - 2，为何 | 青绿 - 浅白 | &gt; | 乌黑 - 浅白 | ？</li>
<li>独热编码 (one-hot encoding)：青绿 - 001、乌黑 - 010、浅白 - 100，一碗水端平，所有取值距离相等，但若取值很多码会很长，且不适应动态出现的新取值</li>
<li>哈希编码 (hash encoding)：用哈希函数将任意输入映射到有限整数范围，码长固定，也能适应动态出现的新取值，但可能存在信息丢失</li>
</ul>
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</section><section vertical="true" data-notes="" lineno="381" class="slide " data-line="381" data-h="4" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征独热编码</h5></div></div>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>preprocessing <span class="token keyword">import</span> LabelBinarizer<span class="token punctuation">,</span> OneHotEncoder

X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token string">'青绿'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'浊响'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'稍蜷'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'稍糊'</span><span class="token punctuation">,</span> <span class="token string">'稍凹'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token string">'浅白'</span><span class="token punctuation">,</span> <span class="token string">'硬挺'</span><span class="token punctuation">,</span> <span class="token string">'清脆'</span><span class="token punctuation">,</span> <span class="token string">'模糊'</span><span class="token punctuation">,</span> <span class="token string">'平坦'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
y <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span><span class="token string">'是'</span><span class="token punctuation">,</span> <span class="token string">'是'</span><span class="token punctuation">,</span> <span class="token string">'否'</span><span class="token punctuation">,</span> <span class="token string">'否'</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token comment"># 类别标记只有两种取值</span>
LabelBinarizer<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>y<span class="token punctuation">)</span><span class="token punctuation">.</span>squeeze<span class="token punctuation">(</span><span class="token punctuation">)</span>
<span class="token punctuation">[</span><span class="token number">1</span> <span class="token number">1</span> <span class="token number">0</span> <span class="token number">0</span><span class="token punctuation">]</span>

enc <span class="token operator">=</span> OneHotEncoder<span class="token punctuation">(</span><span class="token punctuation">)</span>
enc<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">:</span><span class="token number">7</span><span class="token punctuation">]</span><span class="token punctuation">)</span><span class="token punctuation">.</span>toarray<span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token comment"># 对6个类别特征采用独热编码</span>
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span><span class="token punctuation">]</span>
 <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span><span class="token punctuation">]</span>
 <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span><span class="token punctuation">]</span>
 <span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span> <span class="token number">0</span><span class="token punctuation">.</span> <span class="token number">1</span><span class="token punctuation">.</span><span class="token punctuation">]</span><span class="token punctuation">]</span>

enc<span class="token punctuation">.</span>get_feature_names_out<span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token comment"># 独热编码对应的原始特征</span>
<span class="token punctuation">[</span><span class="token string">'x0_乌黑'</span> <span class="token string">'x0_浅白'</span> <span class="token string">'x0_青绿'</span> <span class="token string">'x1_硬挺'</span> <span class="token string">'x1_稍蜷'</span> <span class="token string">'x1_蜷缩'</span> <span class="token string">'x2_沉闷'</span> <span class="token string">'x2_浊响'</span>
 <span class="token string">'x2_清脆'</span> <span class="token string">'x3_模糊'</span> <span class="token string">'x3_清晰'</span> <span class="token string">'x3_稍糊'</span> <span class="token string">'x4_凹陷'</span> <span class="token string">'x4_平坦'</span> <span class="token string">'x4_稍凹'</span> <span class="token string">'x5_硬滑'</span><span class="token punctuation">]</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="412" class="slide " data-line="412" data-h="5" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征缺失处理</h5></div></div>
<div class="threelines column9-border-right-solid head-highlight-1 tr-hover">
<table>
<thead>
<tr>
<th style="text-align:center">编号</th>
<th style="text-align:center">色泽</th>
<th style="text-align:center">根蒂</th>
<th style="text-align:center">敲声</th>
<th style="text-align:center">纹理</th>
<th style="text-align:center">脐部</th>
<th style="text-align:center">触感</th>
<th style="text-align:center">密度</th>
<th style="text-align:center">含糖率</th>
<th style="text-align:center">好瓜</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">1</td>
<td style="text-align:center">青绿</td>
<td style="text-align:center">蜷缩</td>
<td style="text-align:center">浊响</td>
<td style="text-align:center">清晰</td>
<td style="text-align:center">凹陷</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.697</td>
<td style="text-align:center">-</td>
<td style="text-align:center">是</td>
</tr>
<tr>
<td style="text-align:center">2</td>
<td style="text-align:center">乌黑</td>
<td style="text-align:center">蜷缩</td>
<td style="text-align:center">沉闷</td>
<td style="text-align:center">清晰</td>
<td style="text-align:center">凹陷</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.774</td>
<td style="text-align:center">0.376</td>
<td style="text-align:center">是</td>
</tr>
<tr>
<td style="text-align:center">3</td>
<td style="text-align:center">乌黑</td>
<td style="text-align:center">稍蜷</td>
<td style="text-align:center">沉闷</td>
<td style="text-align:center">-</td>
<td style="text-align:center">稍凹</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.666</td>
<td style="text-align:center">0.091</td>
<td style="text-align:center">否</td>
</tr>
<tr>
<td style="text-align:center">4</td>
<td style="text-align:center">浅白</td>
<td style="text-align:center">硬挺</td>
<td style="text-align:center">清脆</td>
<td style="text-align:center">模糊</td>
<td style="text-align:center">平坦</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.245</td>
<td style="text-align:center">0.057</td>
<td style="text-align:center">否</td>
</tr>
</tbody>
</table>
</div>
<p>删除：直接删除有特征缺失的样本，简单粗暴，信息损失</p>
<p>补全：</p>
<ul>
<li>用其他未缺失该特征的样本计算平均数、中位数、众数填充，人为引入噪声</li>
<li>用不存在缺失的其它特征<span class="blue">学习并预测</span>缺失特征的取值，若两者之间无关？</li>
<li>将“缺失”本身作为一种特征取值</li>
</ul>
<p>忽略：采用对缺失特征不敏感的学习模型，如决策树</p>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="439" class="slide " data-line="439" data-h="5" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征缺失处理</h5></div></div>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>impute <span class="token keyword">import</span> SimpleImputer

X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token string">'青绿'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'浊响'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> np<span class="token punctuation">.</span>nan<span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'稍蜷'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'-'</span><span class="token punctuation">,</span> <span class="token string">'稍凹'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token string">'浅白'</span><span class="token punctuation">,</span> <span class="token string">'硬挺'</span><span class="token punctuation">,</span> <span class="token string">'清脆'</span><span class="token punctuation">,</span> <span class="token string">'模糊'</span><span class="token punctuation">,</span> <span class="token string">'平坦'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
<span class="token punctuation">]</span><span class="token punctuation">)</span>

imp_mean <span class="token operator">=</span> SimpleImputer<span class="token punctuation">(</span>strategy<span class="token operator">=</span><span class="token string">'mean'</span><span class="token punctuation">)</span>
imp_mean<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">7</span><span class="token punctuation">:</span><span class="token number">9</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token comment"># 用均值填充</span>
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token number">0.697</span>    <span class="token number">0.17466667</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.774</span>    <span class="token number">0.376</span>     <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.666</span>    <span class="token number">0.091</span>     <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.245</span>    <span class="token number">0.057</span>     <span class="token punctuation">]</span><span class="token punctuation">]</span>

imp_median <span class="token operator">=</span> SimpleImputer<span class="token punctuation">(</span>strategy<span class="token operator">=</span><span class="token string">'median'</span><span class="token punctuation">)</span>
imp_median<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">7</span><span class="token punctuation">:</span><span class="token number">9</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token comment"># 用中位数填充</span>
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token number">0.697</span>    <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.774</span>    <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.666</span>    <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.245</span>    <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">]</span>

imp_frequent <span class="token operator">=</span> SimpleImputer<span class="token punctuation">(</span>missing_values<span class="token operator">=</span><span class="token string">'-'</span><span class="token punctuation">,</span> strategy<span class="token operator">=</span><span class="token string">'most_frequent'</span><span class="token punctuation">)</span>
imp_frequent<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">:</span><span class="token number">7</span><span class="token punctuation">]</span><span class="token punctuation">.</span>astype<span class="token punctuation">(</span><span class="token string">'object'</span><span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token comment"># 用众数填充</span>
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token string">'青绿'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'浊响'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'稍蜷'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'稍凹'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token string">'浅白'</span><span class="token punctuation">,</span> <span class="token string">'硬挺'</span><span class="token punctuation">,</span> <span class="token string">'清脆'</span><span class="token punctuation">,</span> <span class="token string">'模糊'</span><span class="token punctuation">,</span> <span class="token string">'平坦'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">]</span><span class="token punctuation">]</span>

<span class="token comment"># 回归器默认采用BayesianRidge</span>
<span class="token comment"># 可选DecisionTreeRegressor ExtraTreesRegressor KNeighborsRegressor</span>
imp_iter <span class="token operator">=</span> IterativeImputer<span class="token punctuation">(</span><span class="token punctuation">)</span>
imp_iter<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">7</span><span class="token punctuation">:</span><span class="token number">9</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token number">0.697</span>    <span class="token number">0.20908713</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.774</span>    <span class="token number">0.376</span>     <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.666</span>    <span class="token number">0.091</span>     <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.245</span>    <span class="token number">0.057</span>     <span class="token punctuation">]</span><span class="token punctuation">]</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="487" class="slide " data-line="487" data-h="6" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征标准化</h5></div></div>
<p>也称归一化，旨在<span class="blue">消除不同特征间的量纲影响</span></p>
<br>
<p>离差标准化：将原始特征线性变换到 [0, 1] 区间</p>
<p>

$$
\begin{align*}
    x \leftarrow \frac{x - x_\min}{x_\max - x_\min} \in [0,1]
\end{align*}
$$
</p>

<p>最大值标准化：除以该特征的绝对值最大值</p>
<p>

$$
\begin{align*}
    x \leftarrow \frac{x}{\max_{i \in [m]} |x_i|} \in [-1,1]
\end{align*}
$$
</p>

<p>标准差标准化：经过处理的特征近似符合标准正态分布<span class="mathjax-exps">$\Ncal(0,1)$</span></p>
<p>

$$
\begin{align*}
    x \leftarrow \frac{x - \mu}{\sigma}, \quad x \leftarrow \frac{x - x_{\text{median}}}{\sum_{i \in [m]} |x_i - x_{\text{median}}| / m}
\end{align*}
$$
</p>

<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="533" class="slide " data-line="533" data-h="6" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>离差与最大值标准化</h5></div></div>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>preprocessing <span class="token keyword">import</span> MinMaxScaler<span class="token punctuation">,</span> MaxAbsScaler

X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token string">'青绿'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'浊响'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'稍蜷'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'稍糊'</span><span class="token punctuation">,</span> <span class="token string">'稍凹'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token string">'浅白'</span><span class="token punctuation">,</span> <span class="token string">'硬挺'</span><span class="token punctuation">,</span> <span class="token string">'清脆'</span><span class="token punctuation">,</span> <span class="token string">'模糊'</span><span class="token punctuation">,</span> <span class="token string">'平坦'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
<span class="token punctuation">]</span><span class="token punctuation">)</span>

MinMaxScaler<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">7</span><span class="token punctuation">:</span><span class="token number">9</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token comment"># 最大值变成1 同时 最小值变成0</span>
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token number">0.85444234</span>    <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">.</span>            <span class="token number">0.79156328</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.79584121</span>    <span class="token number">0.08436725</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">.</span>            <span class="token number">0</span><span class="token punctuation">.</span>        <span class="token punctuation">]</span><span class="token punctuation">]</span>

MaxAbsScaler<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">7</span><span class="token punctuation">:</span><span class="token number">9</span><span class="token punctuation">]</span><span class="token punctuation">)</span> <span class="token comment"># 最大值变成1</span>
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token number">0.9005168</span>     <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">.</span>            <span class="token number">0.8173913</span> <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.86046512</span>    <span class="token number">0.19782609</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">0.31653747</span>    <span class="token number">0.12391304</span><span class="token punctuation">]</span><span class="token punctuation">]</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="563" class="slide " data-line="563" data-h="6" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>标准差标准化</h5></div></div>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>preprocessing <span class="token keyword">import</span> scale

X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token string">'青绿'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'浊响'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'蜷缩'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'清晰'</span><span class="token punctuation">,</span> <span class="token string">'凹陷'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token string">'乌黑'</span><span class="token punctuation">,</span> <span class="token string">'稍蜷'</span><span class="token punctuation">,</span> <span class="token string">'沉闷'</span><span class="token punctuation">,</span> <span class="token string">'稍糊'</span><span class="token punctuation">,</span> <span class="token string">'稍凹'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token string">'浅白'</span><span class="token punctuation">,</span> <span class="token string">'硬挺'</span><span class="token punctuation">,</span> <span class="token string">'清脆'</span><span class="token punctuation">,</span> <span class="token string">'模糊'</span><span class="token punctuation">,</span> <span class="token string">'平坦'</span><span class="token punctuation">,</span> <span class="token string">'硬滑'</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
<span class="token punctuation">]</span><span class="token punctuation">)</span>

x <span class="token operator">=</span> scale<span class="token punctuation">(</span>X<span class="token punctuation">[</span><span class="token punctuation">:</span><span class="token punctuation">,</span> <span class="token number">7</span><span class="token punctuation">:</span><span class="token number">9</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
x
<span class="token punctuation">[</span><span class="token punctuation">[</span> <span class="token number">0.49236904</span>     <span class="token number">1.22314674</span><span class="token punctuation">]</span>
 <span class="token punctuation">[</span> <span class="token number">0.86589038</span>     <span class="token number">0.74303307</span><span class="token punctuation">]</span>
 <span class="token punctuation">[</span> <span class="token number">0.34199032</span>    <span class="token operator">-</span><span class="token number">0.88592404</span><span class="token punctuation">]</span>
 <span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">1.70024974</span>    <span class="token operator">-</span><span class="token number">1.08025576</span><span class="token punctuation">]</span><span class="token punctuation">]</span>

x<span class="token punctuation">.</span>mean<span class="token punctuation">(</span>axis<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token comment"># 均值接近0</span>
<span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">1.11022302e-16</span>    <span class="token operator">-</span><span class="token number">1.66533454e-16</span><span class="token punctuation">]</span>

x<span class="token punctuation">.</span>std<span class="token punctuation">(</span>axis<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">)</span> <span class="token comment"># 标准差为1</span>
<span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">.</span>    <span class="token number">1</span><span class="token punctuation">.</span><span class="token punctuation">]</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="594" class="slide " data-line="594" data-h="7" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换</h5></div></div>
<p>该步是模型学习前的最后一步，亦有将该步与模型学习融合的做法</p>
<br>
<p>当部分特征冗余甚至有害时，挑选或生成有用的特征子集</p>
<ul>
<li>去除低方差特征，特别是那些在所有样本上取值均不变的特征</li>
<li>先计算 F 检验值、卡方检验值、互信息、线性相关性等统计量，然后据此设立阈值选择特征</li>
<li>引入<span class="mathjax-exps">$\ell_1$</span>等稀疏范数作为约束，将选择特征与模型学习合二为一</li>
<li>通过 PCA、随机投影等降维技术浓缩现有特征</li>
</ul>
<br>
<p>当特征稀缺时，利用现有特征构造新的特征</p>
<ul>
<li>凭经验显式构造：<span class="mathjax-exps">$\xv = [x_1; x_2] \xrightarrow{\Rbb^2 \mapsto \Rbb^6} \xvt = [x_1^2; x_2^2; \sqrt{2} x_1 x_2; \sqrt{2} x_1; \sqrt{2} x_2; 1]$</span></li>
<li>利用核函数<span class="mathjax-exps">$\kappa(\xv, \zv) = \phi(\xv)^\top \phi(\zv)$</span>隐式构造，其中<span class="mathjax-exps">$\phi: \Rbb^d \mapsto \Hbb$</span>是核映射，代表性方法为核方法</li>
<li>利用非线性函数复合<span class="mathjax-exps">$f_n ( f_{n-1} ( \cdots f_2 (f_1 (\xv))))$</span>，代表性方法为神经网络</li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="619" class="slide " data-line="619" data-h="7" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换</h5></div></div>
<p>该步是模型学习前的最后一步，亦有将该步与模型学习融合的做法</p>
<br>
<p>当部分特征冗余甚至有害时，挑选或生成有用的特征子集</p>
<ul>
<li>去除低方差特征，特别是那些在所有样本上取值均不变的特征</li>
<li>先计算 F 检验值、卡方检验值、互信息、线性相关性等统计量，然后据此设立阈值选择特征</li>
<li>引入<span class="mathjax-exps">$\ell_1$</span>等稀疏范数作为约束，将选择特征与模型学习合二为一</li>
<li>通过 PCA、随机投影等降维技术浓缩现有特征</li>
</ul>
<br>
<div class="invis" markdown="1">
<p>当特征稀缺时，利用现有特征构造新的特征</p>
<ul>
<li>凭经验显式构造：<span class="mathjax-exps">$\xv = [x_1; x_2] \xrightarrow{\Rbb^2 \mapsto \Rbb^6} \xvt = [x_1^2; x_2^2; \sqrt{2} x_1 x_2; \sqrt{2} x_1; \sqrt{2} x_2; 1]$</span></li>
<li>利用核函数<span class="mathjax-exps">$\kappa(\xv, \zv) = \phi(\xv)^\top \phi(\zv)$</span>隐式构造，其中<span class="mathjax-exps">$\phi: \Rbb^d \mapsto \Hbb$</span>是核映射，代表性方法为核方法</li>
<li>利用非线性函数复合<span class="mathjax-exps">$f_n ( f_{n-1} ( \cdots f_2 (f_1 (\xv))))$</span>，代表性方法为神经网络</li>
</ul>
</div>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="648" class="slide " data-line="648" data-h="7" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 低方差过滤</h5></div></div>
<p><span class="blue">过滤低方差特征</span>，尤其是那些在所有样本上取值均相同的特征</p>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>feature_selection <span class="token keyword">import</span> VarianceThreshold

X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span> <span class="token comment"># 对西瓜数据集的6个离散类别特征采用了独热编码</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
X<span class="token punctuation">.</span>shape
<span class="token punctuation">(</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token number">19</span><span class="token punctuation">)</span>

<span class="token comment"># 倒数第三列由特征“触感”而来 四个样本都取值“硬滑” 独热编码后都是1 方差为0</span>
XX <span class="token operator">=</span> VarianceThreshold<span class="token punctuation">(</span>threshold<span class="token operator">=</span><span class="token number">0.01</span><span class="token punctuation">)</span><span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">)</span>
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.46</span> <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">]</span>

XX<span class="token punctuation">.</span>shape
<span class="token punctuation">(</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token number">18</span><span class="token punctuation">)</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="679" class="slide " data-line="679" data-h="8" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 方差分析</h5></div></div>
<p>设共有<span class="mathjax-exps">$k$</span>个类别，总样本数为<span class="mathjax-exps">$m = \sum_{i \in [k]} m_i$</span>，总体均值为<span class="mathjax-exps">$\xbar$</span></p>
<p>设第<span class="mathjax-exps">$i$</span>类第<span class="mathjax-exps">$j$</span>个样本为<span class="mathjax-exps">$x_{ij}$</span>，第<span class="mathjax-exps">$i$</span>类的均值为<span class="mathjax-exps">$\xbar_i$</span>，则总体偏差</p>
<p>

$$
\begin{align*}
    \sum_{i \in [k]} &amp; \sum_{j \in [m_i]} (x_{ij} - \xbar)^2 = \sum_{i \in [k]} \sum_{j \in [m_i]} (x_{ij} - \xbar_i + \xbar_i - \xbar)^2 \\
    &amp; = \sum_{i \in [k]} \sum_{j \in [m_i]} [ (x_{ij} - \xbar_i)^2 + (\xbar_i - \xbar)^2 ] + \sum_{i \in [k]} 2 \underbrace{\sum_{j \in [m_i]} (x_{ij} - \xbar_i)}_{=0} (\xbar_i - \xbar) \\
    &amp; = \sum_{i \in [k]} \sum_{j \in [m_i]} (x_{ij} - \xbar_i)^2 + \sum_{i \in [k]} m_i (\xbar_i - \xbar)^2 = SSE + SSB
\end{align*}
$$
</p>

<ul>
<li><span class="mathjax-exps">$SSE$</span>为各类样本与各类均值的偏差之和，越小说明每个类别各自聚集越紧密</li>
<li><span class="mathjax-exps">$SSB$</span>为各类均值与总体的偏差之和，越小说明不同类别的均值差异越小</li>
<li><span class="mathjax-exps">$F = \frac{SSB/(k-1)}{SSE/(m-k)}$</span>越小，说明类别间差异越小</li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="705" class="slide " data-line="705" data-h="8" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 方差分析</h5></div></div>
<p>对任意特征，根据类别标记一分为二计算<span class="mathjax-exps">$F$</span>值，判断差异是否显著</p>
<div class="threelines column9-border-right-solid head-highlight-1 tr-hover">
<table>
<thead>
<tr>
<th style="text-align:center">编号</th>
<th style="text-align:center">色泽</th>
<th style="text-align:center">根蒂</th>
<th style="text-align:center">敲声</th>
<th style="text-align:center">纹理</th>
<th style="text-align:center">脐部</th>
<th style="text-align:center">触感</th>
<th style="text-align:center">密度</th>
<th style="text-align:center">含糖率</th>
<th style="text-align:center">好瓜</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">1</td>
<td style="text-align:center">青绿</td>
<td style="text-align:center">蜷缩</td>
<td style="text-align:center">浊响</td>
<td style="text-align:center">清晰</td>
<td style="text-align:center">凹陷</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.697</td>
<td style="text-align:center">0.460</td>
<td style="text-align:center">是</td>
</tr>
<tr>
<td style="text-align:center">2</td>
<td style="text-align:center">乌黑</td>
<td style="text-align:center">蜷缩</td>
<td style="text-align:center">沉闷</td>
<td style="text-align:center">清晰</td>
<td style="text-align:center">凹陷</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.774</td>
<td style="text-align:center">0.376</td>
<td style="text-align:center">是</td>
</tr>
<tr>
<td style="text-align:center">3</td>
<td style="text-align:center">乌黑</td>
<td style="text-align:center">稍蜷</td>
<td style="text-align:center">沉闷</td>
<td style="text-align:center">稍糊</td>
<td style="text-align:center">稍凹</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.666</td>
<td style="text-align:center">0.091</td>
<td style="text-align:center">否</td>
</tr>
<tr>
<td style="text-align:center">4</td>
<td style="text-align:center">浅白</td>
<td style="text-align:center">硬挺</td>
<td style="text-align:center">清脆</td>
<td style="text-align:center">模糊</td>
<td style="text-align:center">平坦</td>
<td style="text-align:center">硬滑</td>
<td style="text-align:center">0.245</td>
<td style="text-align:center">0.057</td>
<td style="text-align:center">否</td>
</tr>
</tbody>
</table>
</div>
<p>经独热编码后，特征“色泽”变成三个特征，其中一个为色泽是否乌黑</p>
<p>对乌黑</p>
<ul>
<li>好瓜的特征<span class="mathjax-exps">$x_{11} = 0$</span>、<span class="mathjax-exps">$x_{12} = 1$</span>，均值<span class="mathjax-exps">$\xbar_1 = 0.5$</span>、偏差<span class="mathjax-exps">$0.5$</span></li>
<li>坏瓜的特征<span class="mathjax-exps">$x_{21} = 1$</span>、<span class="mathjax-exps">$x_{22} = 0$</span>，均值<span class="mathjax-exps">$\xbar_2 = 0.5$</span>、偏差<span class="mathjax-exps">$0.5$</span>，<span class="mathjax-exps">$SSE = 1$</span></li>
<li>总体均值<span class="mathjax-exps">$\xbar = 0.5$</span>，<span class="mathjax-exps">$SSB = 4 (0.5 - 0.5)^2 = 0$</span>，<span class="mathjax-exps">$F = \frac{0/(2-1)}{1/(4-2)} = 0$</span></li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="732" class="slide " data-line="732" data-h="8" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 方差分析</h5></div></div>
<p>对编号</p>
<ul>
<li>好瓜的特征<span class="mathjax-exps">$x_{11} = 1$</span>、<span class="mathjax-exps">$x_{12} = 2$</span>，均值<span class="mathjax-exps">$\xbar_1 = 1.5$</span>、偏差<span class="mathjax-exps">$0.5$</span></li>
<li>坏瓜的特征<span class="mathjax-exps">$x_{21} = 3$</span>、<span class="mathjax-exps">$x_{22} = 4$</span>，均值<span class="mathjax-exps">$\xbar_2 = 3.5$</span>、偏差<span class="mathjax-exps">$0.5$</span>，<span class="mathjax-exps">$SSE = 1$</span></li>
<li>总体均值<span class="mathjax-exps">$\xbar = 2.5$</span>，<span class="mathjax-exps">$SSB = 2(1.5-2.5)^2 + 2(3.5-2.5)^2 = 4$</span>，<span class="mathjax-exps">$F = \frac{4/(2-1)}{1/(4-2)} = 8$</span></li>
</ul>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>feature_selection <span class="token keyword">import</span> SelectKBest<span class="token punctuation">,</span> f_classif
X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span> <span class="token comment"># 已去掉 与y完全相同的特征 和 方差为零的特征</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
y <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">]</span>
sk <span class="token operator">=</span> SelectKBest<span class="token punctuation">(</span>f_classif<span class="token punctuation">)</span>
sk<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>
sk<span class="token punctuation">.</span>scores_
<span class="token punctuation">[</span> <span class="token number">8</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">0</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>
  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">0</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>
  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">1.71207075</span><span class="token punctuation">,</span> <span class="token number">57.64052606</span><span class="token punctuation">]</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="761" class="slide " data-line="761" data-h="9" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 卡方检验</h5></div></div>
<ul>
<li>若随机变量<span class="mathjax-exps">$X$</span>和<span class="mathjax-exps">$Y$</span>独立，则<span class="mathjax-exps">$p(X,Y) = p(X) p(Y)$</span></li>
<li><span class="mathjax-exps">$|p(X,Y) - p(X) p(Y)|$</span>可衡量<span class="mathjax-exps">$X$</span>和<span class="mathjax-exps">$Y$</span>的独立程度</li>
</ul>
<div class="threelines row4-border-top-solid column1-border-right-solid column3-border-right-solid column1-bold">
<table>
<thead>
<tr>
<th style="text-align:center"></th>
<th style="text-align:center">好瓜</th>
<th style="text-align:center">坏瓜</th>
<th style="text-align:center">边际概率</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">青绿</td>
<td style="text-align:center"><span class="mathjax-exps">$1, ~ (0.5 = 4 \times 0.25 \times 0.5)$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$0, (0.5 = 4 \times 0.25 \times 0.5)$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$0.25$</span></td>
</tr>
<tr>
<td style="text-align:center">乌黑</td>
<td style="text-align:center"><span class="mathjax-exps">$1, ~ (1 = 4 \times 0.5 \times 0.5)$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$1, (1 = 4 \times 0.5 \times 0.5)$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$0.5$</span></td>
</tr>
<tr>
<td style="text-align:center">浅白</td>
<td style="text-align:center"><span class="mathjax-exps">$0, ~ (0.5 = 4 \times 0.25 \times 0.5)$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$1, (0.5 = 4 \times 0.25 \times 0.5)$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$0.25$</span></td>
</tr>
<tr>
<td style="text-align:center">边际概率</td>
<td style="text-align:center"><span class="mathjax-exps">$0.5$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$0.5$</span></td>
<td style="text-align:center"><span class="mathjax-exps">$1$</span></td>
</tr>
</tbody>
</table>
</div>
<ul>
<li><span class="mathjax-exps">$X$</span>是色泽，<span class="mathjax-exps">$Y$</span>是瓜的好坏，总样本数为<span class="mathjax-exps">$4$</span></li>
<li>括号前的<span class="blue">观测频数</span><span class="mathjax-exps">$o = 4 \times p(X,Y)$</span>，括号中的<span class="blue">期望频数</span><span class="mathjax-exps">$e = 4 \times p(X) p(Y)$</span></li>
</ul>
<p>

$$
\begin{align*}
    \chi^2 = \sum_{ij} \frac{(o_{ij}-e_{ij})^2}{e_{ij}} = 4 \times \frac{(1 - 0.5)^2}{0.5} = 2
\end{align*}
$$
</p>

<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="794" class="slide " data-line="794" data-h="9" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 卡方检验</h5></div></div>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>feature_selection <span class="token keyword">import</span> SelectKBest<span class="token punctuation">,</span> chi2
X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
<span class="token punctuation">]</span><span class="token punctuation">)</span>
y <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">]</span>

sk <span class="token operator">=</span> SelectKBest<span class="token punctuation">(</span>chi2<span class="token punctuation">,</span> k<span class="token operator">=</span><span class="token number">1</span><span class="token punctuation">)</span>
sk<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>
sk<span class="token punctuation">.</span>scores_
<span class="token punctuation">[</span><span class="token number">1.6</span>       <span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>
 <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>
 <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">2</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>
 <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token number">0.13165407</span><span class="token punctuation">,</span> <span class="token number">0.48104065</span><span class="token punctuation">]</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><p>独热编码将色泽分成了三个特征，其卡方检验值为 0 + 1 + 1 = 2</p>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="822" class="slide " data-line="822" data-h="10" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 互信息</h5></div></div>
<p>熵 (entropy) 可以度量<span class="blue">随机变量的不确定性</span></p>
<p>

$$
\begin{align*}
    H(X) = - \sum_{i \in [m]} p(x_i) \log p(x_i) = - \Ebb [\log p(X)], \quad 0 \log 0 \triangleq 0
\end{align*}
$$
</p>

<p>当<span class="mathjax-exps">$p(x_1) = \cdots = p(x_m) = \frac{1}{m}$</span>时，熵达到最大值<span class="mathjax-exps">$\log m$</span></p>
<p>拉格朗日函数<span class="mathjax-exps">$L = - \sum_{i \in [m]} p(x_i) \log p(x_i) - \alpha (\sum_{i \in [m]} p(x_i) - 1)$</span>，令</p>
<p>

$$
\begin{align*}
    \frac{\partial L}{\partial p(x_i)} = - \log p(x_i) - 1 - \alpha = 0 ~ \Longrightarrow ~ p(x_i) = \exp(-1-\alpha) = \frac{1}{m}
\end{align*}
$$
</p>

<p>当某个<span class="mathjax-exps">$p(x_i) = 1$</span>、其余为零时，熵达到最小值<span class="mathjax-exps">$0$</span>，此时无不确定性</p>
<p>

$$
\begin{align*}
    H(X) = \sum_{i \in [m]} p(x_i) \log \frac{1}{p(x_i)} \ge \sum_{i \in [m]} p(x_i) \log 1 = 0
\end{align*}
$$
</p>

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</section><section vertical="true" data-notes="" lineno="866" class="slide " data-line="866" data-h="10" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 互信息</h5></div></div>
<p>联合熵：两个随机变量的联合不确定性</p>
<p>

$$
\begin{align*}
    H(X,Y) = - \sum_{i \in [m]} \sum_{j \in [n]} p(x_i,y_j) \log p(x_i,y_j) = - \Ebb [\log p(X,Y)]
\end{align*}
$$
</p>

<p>条件熵：给定一个随机变量的取值后，另一个随机变量的不确定性</p>
<p>

$$
\begin{align*}
    H(X|Y) &amp; = H(X,Y) - H(Y) \\
    &amp; = - \sum_{i \in [m]} \sum_{j \in [n]} p(x_i,y_j) \log p(x_i,y_j) + \sum_{j \in [n]} \class{blue}{p(y_j)} \log p(y_j) \\
    &amp; = - \sum_{i \in [m]} \sum_{j \in [n]} p(x_i,y_j) \log p(x_i,y_j) + \sum_{j \in [n]} \class{blue}{\sum_{i \in [m]} p(x_i,y_j)} \log p(y_j) \\
    &amp; = - \sum_{i \in [m]} \sum_{j \in [n]} p(x_i,y_j) \log p(x_i|y_j) \\
    &amp; = - \Ebb [\log p(X|Y)]
\end{align*}
$$
</p>

<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="900" class="slide " data-line="900" data-h="10" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 互信息</h5></div></div>
<p>互信息：两个随机变量之间的相关程度</p>
<p>

$$
\begin{align*}
    I(X;Y) &amp; = H(X) - H(X|Y) \\
    &amp; = - \sum_{i \in [m]} \class{blue}{p(x_i)} \log p(x_i) + \sum_{i \in [m]} \sum_{j \in [n]} p(x_i,y_j) \log p(x_i|y_j) \\
    &amp; = - \sum_{i \in [m]} \class{blue}{\sum_{j \in [n]} p(x_i,y_j)} \log p(x_i) + \sum_{i \in [m]} \sum_{j \in [n]} p(x_i,y_j) \log \frac{p(x_i,y_j)}{p(y_j)} \\
    &amp; = - \sum_{i \in [m]} \sum_{j \in [n]} p(x_i,y_j) \log \frac{p(x_i)p(y_j)}{p(x_i,y_j)} = \Ebb \left[ \log \frac{p(X,Y)}{p(X)p(Y)} \right]
\end{align*}
$$
</p>

<p>互信息 (交集) 与熵、联合熵 (并集)、条件熵 (差集) 的关系为</p>
<p>

$$
\begin{align*}
    I(X;Y) &amp; = H(X) - H(X|Y) = H(Y) - H(Y|X) \\
    &amp; = H(X) + H(Y) - H(X,Y) \\
    &amp; = H(X,Y) - H(X|Y) - H(Y|X)
\end{align*}
$$
</p>

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</section><section vertical="true" data-notes="" lineno="935" class="slide " data-line="935" data-h="10" data-v="3">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 互信息</h5></div></div>
<p>利用每个特征和类别标记之间的互信息进行挑选</p>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>feature_selection <span class="token keyword">import</span> SelectKBest<span class="token punctuation">,</span> mutual_info_classif

X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
<span class="token punctuation">]</span><span class="token punctuation">)</span>
y <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">]</span>

sk <span class="token operator">=</span> SelectKBest<span class="token punctuation">(</span>mutual_info_classif<span class="token punctuation">)</span>
sk<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">,</span> y<span class="token punctuation">)</span>
sk<span class="token punctuation">.</span>scores_
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<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section data-notes="" lineno="964" class="slide " data-line="964" data-h="11" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 线性相关性</h5></div></div>
<p>

$$
\begin{align*}
    \rho_{xy} = \frac{\cov(x,y)}{\sigma_x \sigma_y} = \frac{\sum_{i \in [m]} (x_i - \xbar)(y_i - \ybar)}{\sqrt{\sum_{i \in [m]} (x_i - \xbar)^2} \sqrt{\sum_{i \in [m]} (y_i - \ybar)^2}}
\end{align*}
$$
</p>

<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np

X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span> <span class="token comment"># 最后一列为y</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
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    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
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<span class="token punctuation">]</span><span class="token punctuation">)</span>

corr <span class="token operator">=</span> np<span class="token punctuation">.</span>corrcoef<span class="token punctuation">(</span>X<span class="token punctuation">,</span> rowvar<span class="token operator">=</span><span class="token boolean">False</span><span class="token punctuation">)</span>
corr<span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">,</span><span class="token punctuation">:</span><span class="token punctuation">]</span>
<span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">0.89442719</span><span class="token punctuation">,</span>  <span class="token number">0</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.57735027</span><span class="token punctuation">,</span>  <span class="token number">0.57735027</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.57735027</span><span class="token punctuation">,</span>
 <span class="token operator">-</span><span class="token number">0.57735027</span><span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">0</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span>  <span class="token number">0.57735027</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.57735027</span><span class="token punctuation">,</span>
 <span class="token operator">-</span><span class="token number">0.57735027</span><span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.57735027</span><span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.57735027</span><span class="token punctuation">,</span>
 <span class="token operator">-</span><span class="token number">0.57735027</span><span class="token punctuation">,</span>  <span class="token number">0.67912971</span><span class="token punctuation">,</span>  <span class="token number">0.9830899</span> <span class="token punctuation">,</span>  <span class="token number">1</span><span class="token punctuation">.</span>        <span class="token punctuation">]</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section><section data-notes="" lineno="998" class="slide " data-line="998" data-h="12" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 稀疏范数</h5></div></div>
<p>范数<span class="mathjax-exps">$\|\cdot\|$</span>：长度概念的推广，对任意标量<span class="mathjax-exps">$\alpha$</span>和向量空间中的<span class="mathjax-exps">$\uv, \vv$</span></p>
<ul>
<li>(半)正定性：<span class="mathjax-exps">$\| \uv \| \ge 0$</span>，且<span class="mathjax-exps">$\| \uv \| = 0$</span>当且仅当<span class="mathjax-exps">$\uv = \zerov$</span></li>
<li>齐次性：<span class="mathjax-exps">$\| \alpha \uv \| = |\alpha| \cdot \| \uv \|$</span></li>
<li>三角不等式：<span class="mathjax-exps">$\| \uv + \vv \| \le \| \uv \| + \| \vv \|$</span></li>
</ul>
<br>
<p>机器学习中常用的是向量的<span class="mathjax-exps">$\ell_p$</span>范数：<span class="mathjax-exps">$\| \wv \|_p \triangleq (\sum_{i \in d} |w_i|^p)^{1/p}$</span></p>
<ul>
<li><span class="mathjax-exps">$\ell_1$</span>范数：<span class="mathjax-exps">$\| \wv \|_1 = \sum_{i \in d} |w_i|$</span>，各元素绝对值之和</li>
<li><span class="mathjax-exps">$\ell_2$</span>范数：<span class="mathjax-exps">$\| \wv \|_2 = \sqrt{\sum_{i \in d} w_i^2}$</span>，各元素平方和的正平方根</li>
<li><span class="mathjax-exps">$\ell_\infty$</span>范数：<span class="mathjax-exps">$\| \wv \|_\infty = \max_{i \in d} |w_i|$</span>，各元素绝对值的最大值</li>
</ul>
<br>
<p>当<span class="mathjax-exps">$0 \le p &lt; 1$</span>时，<span class="mathjax-exps">$\| \cdot \|_p$</span>不再是合法的范数，不满足三角不等式</p>
<ul>
<li><span class="mathjax-exps">$\ell_0$</span>范数：<span class="mathjax-exps">$\| \wv \|_0 = |\{ i \in d \mid w_i \ne 0 \}|$</span>，非零元素的个数</li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="1024" class="slide " data-line="1024" data-h="12" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 稀疏范数</h5></div></div>
<p><span class="mathjax-exps">$\Rbb^2$</span>上的 5 个<span class="mathjax-exps">$\ell_p$</span>范数球<span class="mathjax-exps">$\{ \wv \mid \| \wv \|_p \le t \}$</span></p>
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" title="二维欧氏空间中的5个范数球" class="center top2 bottom2 width75">
<ul>
<li>将<span class="mathjax-exps">$\ell_p~(0 \le p \le 1)$</span>范数球作为学习模型的可行域，可导出稀疏的解</li>
<li>所有<span class="mathjax-exps">$\ell_p~(p \ge 1)$</span>范数球都是凸集，数学性质好</li>
</ul>
<p><span class="mathjax-exps">$\ell_1$</span>唯一既凸且稀疏，将其范数球作为<span class="mathjax-exps">$\Rbb^2$</span>上最小二乘的可行域</p>
<p>

$$
\begin{align*}
    \min_{w_1, w_2} ~ \left \| \begin{bmatrix}
        -2.0011 &amp; -0.8994 \\
        -1.0311 &amp;  0.3146 \\
         0.6900 &amp;  1.7222 \\
         2.3422 &amp; -1.1373 \\
    \end{bmatrix} \begin{bmatrix}
        w_1 \\
        w_2 \\
    \end{bmatrix} - \begin{bmatrix}
        1 \\
        1 \\
        0 \\
        0 \\
    \end{bmatrix} \right\|^2 \quad \st ~ |w_1| + |w_2| \le t
\end{align*}
$$
</p>

<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="1062" class="slide " data-line="1062" data-h="12" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征选择 稀疏范数</h5></div></div>
<ul>
<li>左图中以原点为中心的同心正方形是<span class="mathjax-exps">$\ell_1$</span>范数球的等高线</li>
<li>右图中以原点为中心的同心圆是<span class="mathjax-exps">$\ell_2$</span>范数球的等高线</li>
<li>两图中左边的一系列同心椭圆是<span class="mathjax-exps">$\| \Xv \wv - \yv \|^2$</span>的等高线</li>
</ul>
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" title="目标函数的等高线与l1范数球必然交于正方形顶点" class="center top2 bottom2 width75">
<p>椭圆与正方形必然交在正方形的顶点处，这意味着最优的<span class="mathjax-exps">$w_2 = 0$</span></p>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="1076" class="slide " data-line="1076" data-h="13" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 主成分分析</h5></div></div>
<p>构造<span class="mathjax-exps">$\Rbb^D$</span>中的<span class="mathjax-exps">$d$</span>个标准正交基<span class="mathjax-exps">$\wv_1, \ldots, \wv_d$</span>，将样本投到该<span class="mathjax-exps">$d$</span>维子空间</p>
<p>

$$
\begin{align*}
    \Xv \in \Rbb^{m \times D} \xrightarrow[降维]{\Wv = [\wv_1, \ldots, \wv_d] \in \Rbb^{D \times d}} \Xv \Wv \in \Rbb^{m \times d} \xrightarrow[重构]{\Wv^\top \in \Rbb^{d \times D}} \Xv \Wv \Wv^\top
\end{align*}
$$
</p>

<p>投影到<span class="mathjax-exps">$d ~ (&lt;D)$</span>维子空间存在信息损失，<span class="mathjax-exps">$\Wv$</span>应使得<span class="blue">重构误差尽可能小</span></p>
<p>

$$
\begin{align*}
    \| \Xv &amp; - \Xv \Wv \Wv^\top \|_F^2 = \tr [(\Xv - \Xv \Wv \Wv^\top) (\Xv - \Xv \Wv \Wv^\top)^\top] \\
    &amp; = \tr [\Xv \Xv^\top - 2 \Xv \Wv \Wv^\top \Xv^\top + \Xv \Wv \class{blue}{\mathtip{\Wv^\top \Wv}{等于单位阵\Iv}} \Wv^\top \Xv^\top] \\
    &amp; = \tr [\Xv \Xv^\top - \Xv \Wv \Wv^\top \Xv^\top] \\
    &amp; = \const - \tr [\Wv^\top \Xv^\top \Xv \Wv] \quad \longleftarrow ~ \tr [\Av \Bv] = \tr [\Bv \Av] \\
    &amp; = \const - \wv_1^\top \Xv^\top \Xv \wv_1 - \cdots - \wv_d^\top \Xv^\top \Xv \wv_d
\end{align*}
$$
</p>

<p>

$$
\begin{align*}
    \Longrightarrow \quad \mathop{\mathrm{argmin}}_{\Wv^\top \Wv = \Iv} \| \Xv &amp; - \Xv \Wv \Wv^\top \|_F^2 = \mathop{\mathrm{argmax}}_{\Wv^\top \Wv = \Iv} \sum_{i \in [d]} \wv_i^\top \Xv^\top \Xv \wv_i
\end{align*}
$$
</p>

<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="1120" class="slide " data-line="1120" data-h="13" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 主成分分析</h5></div></div>
<p>

$$
\begin{align*}
    \mathop{\mathrm{argmin}}_{\Wv^\top \Wv = \Iv} \| \Xv &amp; - \Xv \Wv \Wv^\top \|_F^2 = \mathop{\mathrm{argmax}}_{\Wv^\top \Wv = \Iv} \sum_{i \in [d]} \wv_i^\top \Xv^\top \Xv \wv_i
\end{align*}
$$
</p>

<p>假设已平移样本使其中心在原点 (不影响后续模型学习)，即<span class="mathjax-exps">$\onev^\top \Xv = \zerov$</span></p>
<p><span class="mathjax-exps">$\Xv \wv_1$</span>是样本在第<span class="mathjax-exps">$1$</span>个投影方向<span class="mathjax-exps">$\wv_1$</span>上的投影，投影均值<span class="mathjax-exps">$\onev^\top \Xv \wv_1 = 0$</span></p>
<p>

$$
\begin{align*}
    \wv_1^\top \Xv^\top \Xv \wv_1 = \sum_{i \in [m]} (\xv_i^\top \wv_1)^2 = \sum_{i \in [m]} (\xv_i^\top \wv_1 - 0)^2 = \var [\xv_i^\top \wv_1]
\end{align*}
$$
</p>

<p><span class="blue">最小化重构误差</span>等价于<span class="blue">最大化投影方差</span>，即投影后样本尽可能散得开</p>
<p>拉格朗日函数<span class="mathjax-exps">$L = \wv_1^\top \Xv^\top \Xv \wv_1 - \alpha (\wv_1^\top \wv_1 - 1)$</span></p>
<p>

$$
\begin{align*}
    \frac{\partial L}{\partial \wv_1} = 2 \Xv^\top \Xv \wv_1 - 2 \alpha \wv_1 = \zerov \Longrightarrow \mathtip{\wv_1^\top \Xv^\top \Xv \wv_1 = \alpha}{\wv_1应为\Xv^\top \Xv最大特征值对应的特征向量}
\end{align*}
$$
</p>

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</section><section vertical="true" data-notes="" lineno="1164" class="slide " data-line="1164" data-h="13" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 主成分分析</h5></div></div>
<p><span class="blue">主成分分析</span> (PCA)：寻找一系列投影方向 (成分) 使重构误差最小</p>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> sklearn<span class="token punctuation">.</span>decomposition <span class="token keyword">import</span> PCA

X <span class="token operator">=</span> np<span class="token punctuation">.</span>array<span class="token punctuation">(</span><span class="token punctuation">[</span>
    <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.697</span><span class="token punctuation">,</span> <span class="token number">0.460</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.774</span><span class="token punctuation">,</span> <span class="token number">0.376</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">3</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.666</span><span class="token punctuation">,</span> <span class="token number">0.091</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
    <span class="token punctuation">[</span><span class="token number">4</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0</span><span class="token punctuation">,</span> <span class="token number">1</span><span class="token punctuation">,</span> <span class="token number">0.245</span><span class="token punctuation">,</span> <span class="token number">0.057</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
<span class="token punctuation">]</span><span class="token punctuation">)</span>

pca <span class="token operator">=</span> PCA<span class="token punctuation">(</span>n_components<span class="token operator">=</span><span class="token number">2</span><span class="token punctuation">)</span> <span class="token comment"># 降到2维</span>
XX <span class="token operator">=</span> pca<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">)</span>
XX
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">2.00117642</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.8994997</span> <span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">1.03113008</span><span class="token punctuation">,</span>  <span class="token number">0.31462009</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span> <span class="token number">0.69000731</span><span class="token punctuation">,</span>  <span class="token number">1.72221775</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span> <span class="token number">2.34229919</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">1.13733814</span><span class="token punctuation">]</span><span class="token punctuation">]</span>
np<span class="token punctuation">.</span>linalg<span class="token punctuation">.</span>norm<span class="token punctuation">(</span>X <span class="token operator">-</span> pca<span class="token punctuation">.</span>inverse_transform<span class="token punctuation">(</span>XX<span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token comment"># 计算重构误差</span>
<span class="token number">1.2626787274464972</span>

pca <span class="token operator">=</span> PCA<span class="token punctuation">(</span>n_components<span class="token operator">=</span><span class="token number">3</span><span class="token punctuation">)</span> <span class="token comment"># 降到3维</span>
XX <span class="token operator">=</span> pca<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">)</span>
XX
<span class="token punctuation">[</span><span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">2.00117642</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.8994997</span> <span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.60604575</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">1.03113008</span><span class="token punctuation">,</span>  <span class="token number">0.31462009</span><span class="token punctuation">,</span>  <span class="token number">1.00575703</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span> <span class="token number">0.69000731</span><span class="token punctuation">,</span>  <span class="token number">1.72221775</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">0.46027295</span><span class="token punctuation">]</span><span class="token punctuation">,</span>
 <span class="token punctuation">[</span> <span class="token number">2.34229919</span><span class="token punctuation">,</span> <span class="token operator">-</span><span class="token number">1.13733814</span><span class="token punctuation">,</span>  <span class="token number">0.06056167</span><span class="token punctuation">]</span><span class="token punctuation">]</span>

np<span class="token punctuation">.</span>linalg<span class="token punctuation">.</span>norm<span class="token punctuation">(</span>X <span class="token operator">-</span> pca<span class="token punctuation">.</span>inverse_transform<span class="token punctuation">(</span>XX<span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token comment"># 计算重构误差</span>
<span class="token number">1.7568561344411767e-15</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="1205" class="slide " data-line="1205" data-h="14" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 随机投影</h5></div></div>
<p>Johnson–Lindenstrauss 定理：给定<span class="mathjax-exps">$\epsilon \in (0,1)$</span>和正整数<span class="mathjax-exps">$m$</span>，设<span class="mathjax-exps">$d$</span>满足</p>
<p>

$$
\begin{align*}
    d \ge 4 (\epsilon^2/2 - \epsilon^3/3)^{-1} \ln m
\end{align*}
$$
</p>

<p>则对<span class="mathjax-exps">$\Rbb^D$</span>中的任意<span class="mathjax-exps">$m$</span>个点组成的集合<span class="mathjax-exps">$\Scal$</span>，存在可在随机多项式时间内得到的线性映射<span class="mathjax-exps">$f: \Rbb^D \mapsto \Rbb^d$</span>使得对任意<span class="mathjax-exps">$\uv, \vv \in \Scal$</span>有</p>
<p>

$$
\begin{align*}
    (1 - \epsilon) \| \uv -\vv \|^2 \le \| f(\uv) - f(\vv) \|^2 \le (1 + \epsilon) \| \uv - \vv \|^2
\end{align*}
$$
</p>

<br>
<p>JL 定理表明<span class="blue">高维空间中的点集映射到低维空间可相对保持距离</span></p>
<br>
<p>投影矩阵通常采用</p>
<ul>
<li>高斯随机矩阵：每个元素从高斯随机变量<span class="mathjax-exps">$\Ncal(0,1/d)$</span>中采样</li>
<li>稀疏随机矩阵：每个元素以<span class="mathjax-exps">$1/2s$</span>的概率取<span class="mathjax-exps">$\pm \sqrt{s/d}$</span>，以<span class="mathjax-exps">$1-1/s$</span>的概率取<span class="mathjax-exps">$0$</span></li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="1246" class="slide " data-line="1246" data-h="14" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 随机投影</h5></div></div>
<pre data-role="codeBlock" data-info="python {.line-numbers}" class="language-python line-numbers"><span class="token keyword">import</span> numpy <span class="token keyword">as</span> np
<span class="token keyword">from</span> scipy<span class="token punctuation">.</span>spatial <span class="token keyword">import</span> distance

X <span class="token operator">=</span> np<span class="token punctuation">.</span>random<span class="token punctuation">.</span>rand<span class="token punctuation">(</span><span class="token number">100</span><span class="token punctuation">,</span> <span class="token number">10000</span><span class="token punctuation">)</span>
D1 <span class="token operator">=</span> distance<span class="token punctuation">.</span>cdist<span class="token punctuation">(</span>X<span class="token punctuation">,</span> X<span class="token punctuation">,</span> <span class="token string">'euclidean'</span><span class="token punctuation">)</span> <span class="token comment"># 原样本的成对距离矩阵</span>

transformer <span class="token operator">=</span> random_projection<span class="token punctuation">.</span>GaussianRandomProjection<span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token comment"># 高斯随机矩阵</span>
XX <span class="token operator">=</span> transformer<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">)</span>
D2 <span class="token operator">=</span> distance<span class="token punctuation">.</span>cdist<span class="token punctuation">(</span>XX<span class="token punctuation">,</span> XX<span class="token punctuation">,</span> <span class="token string">'euclidean'</span><span class="token punctuation">)</span> <span class="token comment"># 投影后样本的成对距离矩阵</span>

XX<span class="token punctuation">.</span>shape
<span class="token punctuation">(</span><span class="token number">100</span><span class="token punctuation">,</span> <span class="token number">3947</span><span class="token punctuation">)</span>

np<span class="token punctuation">.</span>linalg<span class="token punctuation">.</span>norm<span class="token punctuation">(</span>D1 <span class="token operator">-</span> D2<span class="token punctuation">,</span> <span class="token builtin">ord</span><span class="token operator">=</span><span class="token string">'fro'</span><span class="token punctuation">)</span> <span class="token comment"># 两个成对距离矩阵差的F范数</span>
<span class="token number">46.74573519884732</span>

transformer <span class="token operator">=</span> random_projection<span class="token punctuation">.</span>GaussianRandomProjection<span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token comment"># 稀疏随机矩阵</span>
XX <span class="token operator">=</span> transformer<span class="token punctuation">.</span>fit_transform<span class="token punctuation">(</span>X<span class="token punctuation">)</span>
D2 <span class="token operator">=</span> distance<span class="token punctuation">.</span>cdist<span class="token punctuation">(</span>XX<span class="token punctuation">,</span> XX<span class="token punctuation">,</span> <span class="token string">'euclidean'</span><span class="token punctuation">)</span> <span class="token comment"># 投影后样本的成对距离矩阵</span>

np<span class="token punctuation">.</span>linalg<span class="token punctuation">.</span>norm<span class="token punctuation">(</span>D1 <span class="token operator">-</span> D2<span class="token punctuation">,</span> <span class="token builtin">ord</span><span class="token operator">=</span><span class="token string">'fro'</span><span class="token punctuation">)</span> <span class="token comment"># 两个成对距离矩阵差的F范数</span>
<span class="token number">43.819210159457796</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></pre><div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section><section data-notes="" lineno="1277" class="slide " data-line="1277" data-h="15" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换</h5></div></div>
<p>该步是模型学习前的最后一步，亦有将该步与模型学习融合的做法</p>
<br>
<div class="invis" markdown="1">
<p>当部分特征冗余甚至有害时，挑选或生成有用的特征子集</p>
<ul>
<li>去除低方差特征，特别是那些在所有样本上取值均不变的特征</li>
<li>先计算 F 检验值、卡方检验值、互信息、线性相关性等统计量，然后据此设立阈值选择特征</li>
<li>引入<span class="mathjax-exps">$\ell_1$</span>等稀疏范数作为约束，将选择特征与模型学习合二为一</li>
<li>通过 PCA、随机投影等降维技术浓缩现有特征</li>
</ul>
</div>
<br>
<p>当特征稀缺时，利用现有特征构造新的特征</p>
<ul>
<li>凭经验显式构造：<span class="mathjax-exps">$\xv = [x_1; x_2] \xrightarrow{\Rbb^2 \mapsto \Rbb^6} \xvt = [x_1^2; x_2^2; \sqrt{2} x_1 x_2; \sqrt{2} x_1; \sqrt{2} x_2; 1]$</span></li>
<li>利用核函数<span class="mathjax-exps">$\kappa(\xv, \zv) = \phi(\xv)^\top \phi(\zv)$</span>隐式构造，其中<span class="mathjax-exps">$\phi: \Rbb^d \mapsto \Hbb$</span>是核映射，代表性方法为核方法</li>
<li>利用非线性函数复合<span class="mathjax-exps">$f_n ( f_{n-1} ( \cdots f_2 (f_1 (\xv))))$</span>，代表性方法为神经网络</li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="1306" class="slide " data-line="1306" data-h="15" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 构造新特征</h5></div></div>
<p>凭经验显式构造映射<span class="mathjax-exps">$\phi$</span>，如二次多项式特征：</p>
<p>

$$
\begin{align*}
    \xv = [x_1; x_2] \xrightarrow{\phi: ~ \Rbb^2 \mapsto \Rbb^6} \xvt = [x_1^2; x_2^2; \sqrt{2} x_1 x_2; \sqrt{2} x_1; \sqrt{2} x_2; 1]
\end{align*}
$$
</p>

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<ul>
<li>原本圆内是一类样本，圆外是另一类样本，它们无法<span class="blue">线性可分</span></li>
<li>只需将<span class="mathjax-exps">$[x_1; x_2] \mapsto [z_1 = x_1^2; z_2 = x_2^2]$</span>，在新的<span class="mathjax-exps">$(z_1,z_2)$</span>空间中就线性可分了</li>
</ul>
<p>

$$
\begin{align*}
    x_1^2 + x_2^2 \le t ~ \longrightarrow ~ z_1 + z_2 \le t
\end{align*}
$$
</p>

<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section data-notes="" lineno="1339" class="slide " data-line="1339" data-h="16" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 核技巧</h5></div></div>
<p>显式构造映射<span class="mathjax-exps">$\phi$</span>过于依赖使用者的姿势水平，如果后续模型的学习</p>
<ul>
<li>不需要样本<span class="mathjax-exps">$\xv$</span>的新特征的显式表示<span class="mathjax-exps">$\phi(\xv)$</span></li>
<li>只用到新特征空间的内积<span class="mathjax-exps">$\phi(\xv)^\top \phi(\zv)$</span></li>
</ul>
<p>那么对映射<span class="mathjax-exps">$\phi([x_1;x_2]) = [x_1^2; x_2^2; \sqrt{2} x_1 x_2; \sqrt{2} x_1; \sqrt{2} x_2; 1]$</span>和样本<span class="mathjax-exps">$\xv,\zv$</span>有</p>
<p>

$$
\begin{align*}
    \phi(\xv)^\top \phi(\zv) &amp; = x_1^2 z_1^2 + x_2^2 z_2^2 + 2 x_1 x_2 z_1 z_2 + 2 x_1 z_1 + 2 x_2 z_2 + 1 \\
    &amp; = (x_1 z_1 + x_2 z_2 + 1)^2 \\
    &amp; = (\xv^\top \zv + 1)^2 \\
    &amp; = \kappa (\xv, \zv)
\end{align*}
$$
</p>

<p>换言之构造新特征有两套方案：</p>
<ul>
<li>显式构造核映射<span class="mathjax-exps">$\phi([x_1;x_2]) = [x_1^2; x_2^2; \sqrt{2} x_1 x_2; \sqrt{2} x_1; \sqrt{2} x_2; 1]$</span></li>
<li>通过在原空间直接定义<span class="blue">核函数</span><span class="mathjax-exps">$\kappa (\xv, \zv) = (\xv^\top \zv + 1)^2$</span>隐式构造，这称为核技巧</li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section><section data-notes="" lineno="1370" class="slide " data-line="1370" data-h="17" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 核函数</h5></div></div>
<p>核函数<span class="mathjax-exps">$\kappa(\cdot, \cdot)$</span>是双变量对称函数，即<span class="mathjax-exps">$\kappa(\xv, \zv) = \kappa(\zv, \xv)$</span>，常见的有：</p>
<ul>
<li>线性核<span class="mathjax-exps">$\kappa (\xv, \zv) = \xv^\top \zv$</span>，相当于用了恒等核映射<span class="mathjax-exps">$\phi(\xv) = \xv$</span></li>
<li>多项式核<span class="mathjax-exps">$\kappa (\xv, \zv) = (\xv^\top \zv + k)^d$</span>，<span class="mathjax-exps">$k = 0$</span>则为齐次多项式核，<span class="mathjax-exps">$d \in \Zbb_+$</span></li>
<li>高斯核<span class="mathjax-exps">$\kappa (\xv, \zv) = \exp (- \| \xv - \zv \|^2 / 2 \sigma^2)$</span>，<span class="mathjax-exps">$\sigma &gt; 0$</span>称为高斯核的带宽 (width)</li>
<li>拉普拉斯核<span class="mathjax-exps">$\kappa (\xv, \zv) = \exp (- \| \xv - \zv \| / \sigma)$</span>，<span class="mathjax-exps">$\sigma &gt; 0$</span></li>
<li>Sigmoid 核<span class="mathjax-exps">$\kappa (\xv, \zv) = \tanh (\beta \xv^\top \zv + \theta)$</span>，<span class="mathjax-exps">$\tanh$</span>为双曲正切函数，<span class="mathjax-exps">$\beta &gt; 0$</span>，<span class="mathjax-exps">$\theta &lt; 0$</span></li>
</ul>
<br>
<p>将 PCA 中的样本<span class="mathjax-exps">$\xv$</span>用<span class="mathjax-exps">$\phi(\xv)$</span>替代，就得到了核 PCA，先升维再降维</p>
<br>
<p>PCA：<span class="mathjax-exps">$\max_{\|\wv\|_2^2 = 1} \wv^\top \Xv^\top \Xv \wv$</span> → 核 PCA：<span class="mathjax-exps">$\max_{\|\wv\|_2^2 = 1} \wv^\top \phi(\Xv)^\top \phi(\Xv) \wv$</span></p>
<p>其中<span class="mathjax-exps">$\Xv = \begin{bmatrix} \xv_1^\top \\ \vdots \\ \xv_m^\top \end{bmatrix}$</span>、<span class="mathjax-exps">$\phi(\Xv) = \begin{bmatrix} \phi(\xv_1)^\top \\ \vdots \\ \phi(\xv_m)^\top \end{bmatrix}$</span>，注意两个<span class="mathjax-exps">$\wv$</span>的维度不一样</p>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="1394" class="slide " data-line="1394" data-h="17" data-v="1">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 核 PCA</h5></div></div>
<p>问题：如何让模型中只出现内积<span class="mathjax-exps">$\phi(\xv_i)^\top \phi(\xv_j)$</span>的形式？</p>
<p>对<span class="mathjax-exps">$\wv$</span>做正交分解<span class="mathjax-exps">$\wv = \sum_{i \in [m]} \alpha_i \phi(\xv_i) + \vv = \phi(\Xv)^\top \alphav + \vv$</span>，其中</p>
<p>

$$
\begin{align*}
    \vv \perp \span \{ \phi(\xv_1), \ldots, \phi(\xv_m) \} ~ \Longrightarrow ~ \phi(\Xv) \vv = \zerov
\end{align*}
$$
</p>

<p>于是</p>
<p>

$$
\begin{align*}
    &amp; \|\wv\|_2^2 = \alphav^\top \phi(\Xv) \phi(\Xv)^\top \alphav + \vv^\top \vv = \alphav^\top \Kv \alphav + \vv^\top \vv \\
    &amp; \phi(\Xv) \wv = \phi(\Xv) (\phi(\Xv)^\top \alphav + \vv) = \phi(\Xv) \phi(\Xv)^\top \alphav = \Kv \alpha
\end{align*}
$$
</p>

<p>其中<span class="mathjax-exps">$\Kv = \phi(\Xv) \phi(\Xv)^\top = \begin{bmatrix} \phi(\xv_1)^\top \phi(\xv_1) &amp; \cdots &amp; \phi(\xv_1)^\top \phi(\xv_m) \\ \vdots &amp; \ddots &amp; \vdots \\ \phi(\xv_m)^\top \phi(\xv_1) &amp; \cdots &amp; \phi(\xv_m)^\top \phi(\xv_m) \end{bmatrix}$</span>为核矩阵</p>
<p>核 PCA 可重写为<span class="mathjax-exps">$\max_{\alphav, \vv} ~ \alphav^\top \Kv \Kv \alphav, \quad \st ~ \alphav^\top \Kv \alphav + \vv^\top \vv = 1$</span></p>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section><section vertical="true" data-notes="" lineno="1431" class="slide " data-line="1431" data-h="17" data-v="2">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 核 PCA</h5></div></div>
<p>核 PCA：<span class="mathjax-exps">$\max_{\alphav, \vv} ~ \alphav^\top \Kv \Kv \alphav, \quad \st ~ \alphav^\top \Kv \alphav + \vv^\top \vv = 1$</span></p>
<p>设最优解为<span class="mathjax-exps">$(\alphav_\star, ~ \vv_\star)$</span>，下面说明<span class="mathjax-exps">$\vv_\star = \zerov$</span></p>
<ul>
<li>若<span class="mathjax-exps">$\vv_\star^\top \vv_\star = c &gt; 0$</span>，则<span class="mathjax-exps">$\alphav_\star^\top \Kv \alphav_\star = 1 - c &lt; 1$</span></li>
<li><span class="mathjax-exps">$(\alphav_0 = 1 / \sqrt{1-c} ~ \alphav_\star, ~ \vv_0 = \zerov)$</span>也是一组可行解</li>
<li>显然<span class="mathjax-exps">$\alphav_0^\top \Kv \Kv \alphav_0 = \alphav_\star^\top \Kv \Kv \alphav_\star / (1-c) &gt; \alphav_\star^\top \Kv \Kv \alphav_\star$</span>，这与<span class="mathjax-exps">$\alphav_\star$</span>的最优性矛盾</li>
</ul>
<br>
<p>核 PCA 的最终形式为<span class="mathjax-exps">$\max_\alphav ~ \alphav^\top \Kv \Kv \alphav, \quad \st ~ \alphav^\top \Kv \alphav = 1$</span></p>
<p>通过拉格朗日乘子法求得系数<span class="mathjax-exps">$\alphav$</span>后，样本<span class="mathjax-exps">$\xv_j$</span>在成分<span class="mathjax-exps">$\wv$</span>上的投影为</p>
<p>

$$
\begin{align*}
    \wv^\top \phi(\xv_j) = \sum_{i \in [m]} \alpha_i \phi(\xv_i)^\top \phi(\xv_j) = \sum_{i \in [m]} \alpha_i \kappa (\xv_i, \xv_j)
\end{align*}
$$
</p>

<p>通过核 PCA 可以看出，全程我们都用不到<span class="mathjax-exps">$\phi(\cdot)$</span>，只需要<span class="mathjax-exps">$\kappa(\cdot, \cdot)$</span></p>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
</section></section><section data-notes="" lineno="1463" class="slide " data-line="1463" data-h="18" data-v="0">
<div class="header"><img class="hust" src=""><div class="title"><hr class="hr_top"><h5>特征变换 非线性复合</h5></div></div>
<p>设<span class="mathjax-exps">$\sigma_1, \ldots, \sigma_l$</span>是一系列简单的非线性函数，如<span class="mathjax-exps">$[x]_+ = \max \{ x, 0 \}$</span></p>
<p>一个简单的<span class="mathjax-exps">$l$</span>层神经网络：</p>
<p>

$$
\begin{align*}
    \hv_1 &amp; = \sigma_1(\Wv_1 \xv + \bv_1) \\
    \hv_2 &amp; = \sigma_2(\Wv_2 \hv_1 + \bv_2) \\
    &amp; \vdots \\
    \hv_{l-1} &amp; = \sigma_{l-1}(\Wv_{l-1} \hv_{l-2} + \bv_{l-1}) \\
    f(\xv) &amp; = \sigma_l (\Wv_l \hv_{l-1} + \bv_l)
\end{align*}
$$
</p>

<p>前<span class="mathjax-exps">$l-1$</span>层复合为特征变换，最后一层拟合类别标记，即为模型学习</p>
<br>
<p>对比：</p>
<ul>
<li>核方法毕其功于一役，一个核函数直接搞定问题，难点在于<span class="blue">如何设计核函数</span></li>
<li>神经网络步步为营，一步一个小目标，难点在于<span class="blue">如何设计一系列非线性函数</span></li>
</ul>
<div class="footer"><hr class="hr_bottom"><div class="multi_column"><h6 class="bottom_left">图神经网络导论</h6><h6 class="bottom_center">机器学习</h6><h6 class="bottom_right">tengzhang@hust.edu.cn</h6></div></div>
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